Trigonometry Course by Dennis Davis

About this course

Strengthen your math foundation by learning how to use trigonometry with confidence, from the first idea of an angle to the tools needed to solve real problems. This free online course is built to help you move beyond memorizing formulas and start understanding what the functions mean, how they relate to triangles and circles, and why they behave the way they do.

You will develop a clear sense of angles in standard position, the difference between degrees and radians, and how to convert and interpret each in practical settings. With a solid geometry refresh, you connect right-triangle thinking to coordinate geometry, distance formulas, and the Pythagorean theorem, creating the bridge that makes trig ratios feel intuitive instead of abstract. From there, the course guides you into the unit circle, showing how sine, cosine, and tangent extend to all quadrants and how common angle values can be understood, verified, and used efficiently.

As you progress, you will gain skill with calculators in both degree and radian modes, learn how trigonometric functions behave on graphs, and understand domain, range, and key features such as zeros, asymptotes, and periodicity. This knowledge makes it easier to interpret models and predict how changing parameters affects a curve, which is essential for many school topics and exam problems.

The course also builds mathematical maturity through inverse functions and inverse trigonometric functions, helping you interpret answers correctly and avoid common traps with principal values. You then apply trigonometry to triangle solving beyond right triangles, using laws of sines and cosines and understanding when solutions are unique, ambiguous, or impossible. To finish, you develop fluency with identities, including Pythagorean, sum and difference, double-angle, and half-angle relationships, reinforcing the logic of proofs and the algebraic flexibility needed in advanced math.

With short checks and exercises throughout, this course is ideal for students who want stronger grades, test readiness, or a reliable path into precalculus, physics, and engineering fundamentals.